Rectangles 6279

Reduce the dimensions of the rectangle with dimensions of 21 cm and 1.4 dm in a ratio of 4:7. In what proportion will the areas of both rectangles be?

Correct answer:

r =  49:16 cm

Step-by-step explanation:

$$\begin{gathered} a=21\text{cm} \\ b=1.4\text{dm}\to \text{cm}=1.4\cdot 10\text{cm}=14\text{cm} \\ k=\frac{4}{7}\doteq 0.5714 \\ c=a\cdot \frac{4}{7}=21\cdot \frac{4}{7}=\frac{21\cdot 4}{7}=\frac{84}{7}=12\text{cm} \\ d=b\cdot \frac{4}{7}=14\cdot \frac{4}{7}=\frac{14\cdot 4}{7}=\frac{56}{7}=8\text{cm} \\ {S}_1=a\cdot b=21\cdot 14=294{\text{cm}}^2 \\ {S}_2=c\cdot d=12\cdot 8=96{\text{cm}}^2 \\ r=S_1/S_2=294/96=\frac{49}{16}\text{cm}=3.0625=49:16\text{cm} \end{gathered}$$

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